Constraint Handling

Abstract

In this chapter we consider the issue of constraint handling by evolutionary algorithms. This issue has great practical relevance because many practical problems are constrained. It is also a theoretically challenging subject since a great deal of intractable problems (NP-hard, NP-complete, etc.) are constrained. The presence of constraints has the effect that not all possible combinations of variable values represent valid solutions to the problem at hand. Unfortunately, constraint handling is not straightforward in an EA, because the variation operators (mutation and recombination) are typically “blind” to constraints. That is, there is no guarantee that even if the parents satisfy some constraints, the offspring will satisfy them as well. In this chapter we elaborate on the notion of constrained problems and distinguish two different types: constrained optimisation problems and constraint satisfaction problems. (This elaboration requires clarifying some basic notions, leading to definitions that implicitely have been used in earlier chapters.) Based on this classification of constrained problems, we discuss what constraint handling means from an EA perspective, and review the most commonly applied EA techniques to treat constraints. Analysing these techniques, we identify a number of common features and arrive at the conclusion that the presence of constraints is not harmful, but rather helpful in that it provides extra information that EAs can utilise.